I read through the guidelines and I'm trying to decide if I need to report this book with a problem.  I have a lot of transactions (well over 100) and this would be my first time doing that so it's not like I am super picky.  The book that arrived is a paperback from 1960 and the only thing holding the pages in place is a piece of packing tape on the spine.  When you open the book it is clear that the pages are separated from the spine and each other.  It's readable but definitely not postable again.  Do I report it?

The pages must be attached. To quote Melanie from another post - If the book was unpostable before the tape was applied, tape does not return a book to being postable.

You should mark it RWAP (Received with a problem). You can, but you don't have to, ask for your credit back. In this case, I probably would.

Yeah, that ^   Sometimes with older books the glue can fail during shipping from the heat of sitting in a truck all day or rough handling but if it's taped you know it was like that when they mailed it. 

What they said.  The spine and pages must be intact to be postable, and tape cannot return an unpostable book to postability.  Old glue can be damaged during shipping (depending on wrapper) but the tape indicates a pre-existing problem.  RWAP.

For PBS purposes, the only legit purpose for tape is to reinforce a lightly damaged book (not yet unpostable) so as to delay it's unpostable status.  Once a book is unpostable, the addition of tape cannot make it postable again.